OK so, your shape is a pentagon, how I like to do this and how I was taught to make it easier was divide the pentagon or what ever shape it is in to smaller easier shapes like triangles and rectangles. so this one looks like a diamond. You see the part where it say 4 inches and 8 inches, well we are going to cut it off there and find the area of that first with is 4x8=32
next we are going up to where it looks like a trapezoid and we are going to divide that into a triangle and a rectangle. Lets start with the rectangle 5.3x4= 21.2 now we move on to the triangle and the formula for that id A=1/2BxH but we can find 1/2 of the H instead of 1/2 of the B (B=base H=height) so 1/2 h = 2 so 2x2.7=5.4 now we add them all together:
5.4+32+21.2= 58.6 so the answer is: 58.6 in.^2